Options. Selective non-liposuction options for fat removal are on the rise. Technologies using radio frequency (thermage), ultrasound (ulthera) laser lipolysis (smart lipo), mesotherapy (kythera) are used for subcutaneous fat reduction and/or skin tightening but are primarily for use elsewhere or without fda approval at this time for facial fat removal. Buccal fat extraction is also another method.
Time. One of the cardinal signs of aging is the loss of facial fat. In general, what is an annoyance now, will become a blessing later. The facial fat is genetically programmed. While weight loss can help, it sounds like you would lose additional fat in areas that would not be desireable. Only surgery can selectively remove fat, but the face is not the safest area for liposuction.
Why not lipo? Liposuction is very easy to do under local anesthesia in the neck area if the skin tone is good. A very common procedure is to remove some fat from the neck and transfer into the cheeks especially the "tear trough" groove in the lower eyelid area that constributes to a tired look. None of the few options that work for nonsurgical fat reduction are ideal for the face/neck area.
Facelift. By asps plastic surgeon.
May be genetic. May be difficult, since some deposits tend to be genetic or within your family. If thin everywhere else, may not actually be caused by fat. I would see your physician to find out what is causing the appearance you describe.